SSC CGL Tier l 2023 Question Paper Shift 3 (July 21st)

Simplify the following expression.
$$\left[\left(1 + p\right)\left(1 + p^{2}\right)\left(1 + p^{4}\right)\left(1 + p^{8}\right)\left(1 + p^{16}\right)\left(1 - p\right) - 1 \right]$$

$$S_{1}$$ and $$S_{2}$$ are two stations which are 195 km apart. A train starts from $$S_{1}$$ at 4:00 pm and moves towards $$S_{2}$$ at the speed of 65 km/h. Another train starts from $$S_{2}$$ at 5:00 pm and moves towards $$S_{1}$$ at the speed of 35 km/h. At what time will the two trains meet?

Two chords AB and CD of a circle meet inside the circle at point P. If AP= 12 cm, AB = 20 cm and CP = 16 cm, then CD =?

There are 15 students in a class. Their average weight is 40 kg. When one student leaves the class, the average weight is 39.5 kg. What is the weight of the student who left the class (where kg means kilogram)?

In $$\triangle XYZ$$, right angled at Y. if $$\sin X = \frac{1}{2}$$, find the value of $$\cos X \cos Z + \sin X \sin Z$$.

Rekha alone can complete a work in 16 days, and B in a alone can complete the same work in 12 days. Starting with Rekha, they work on alternate days. The total work will be completed in:

A certain amount is lent at x% p.a. simple interest for 3 years. Instead, if the amount was lent at 3x% p.a. simple interest for 'y' more years, then the simple interest would have been seven times the earlier interest. What is the value of y?

The value of $$\left(16 + 14\right) \div 2 - 12 + 16 \times 4 - 28 + 13 \left(- 16 + 13\right)$$ is:

Study the given table and answer the question that follows.
The table gives the number of graduate students enrolled in 4 different colleges A, B, C, and D in a city over the years 2010 to 2014 and also the number of students who passed in the final examination during these years.

Find the ratio of the average of students enrolled from college D to the average of students who passed from college D over all the years.

If x and y are positive numbers such that x - y = 5 and xy = 150, then the value of (x + y) is: